Shortly after Pearl Harbor, a 12-year-old boy walked into an Arizona recruiting office and said, “I want to join the Army and shoot some Japs. Sure, I’m 17 years old. You enlist men 17 years old, don’t you? I don’t need my mother’s consent … I’m a midget.”

He didn’t get in, but other boys did. In 1942 the Marines issued an honorable discharge to William Holle of Eau Claire, Wis., who had enlisted the previous year at age 12. And 13-year-old Jackie MacInnes of Medford, Mass., took his older brother’s birth certificate to a Boston enlistment office, forged his parents’ signatures on the consent papers, and reported for duty at Newport, R.I. “Everything was going fine,” ran one news report, “until he wrote a letter home.” His parents came to pick him up.

At least one underage enlistee escaped detection — in 1988 Ronald Reagan signed a special bill granting disability benefits to Calvin L. Graham, above, a Marine veteran injured at Guadalcanal. The Navy had denied them because he’d lied about his age when enlisting. He was 12.

An attractive woman approaches Sylvester in a bar. She has a proposition: For a single payment of £50, he can have a passionate weeklong holiday with her in Nice. Everything else is covered: travel tickets, a first-class hotel, and her attentions. There’s one further condition. She’ll shortly say something important, which we’ll call the “key.” If the key is true, then she keeps the £50 and Sylvester gets the holiday at no further cost, as explained. If the key is false, then Sylvester must accept the £50 back, but he still gets the week’s holiday with her for free.

“How can he lose?” asks Peter Cave in How to Think Like a Bat (2011). “Either way, with regard to whether the key is true or not, he is bound to have the splendid trip and the passion. At worst, it costs him a mere £50.” He gives her the £50, and she gives him the key:

Either I shall return the £50 or you will pay me £1 million.

For an either/or statement to be false, both elements must be false. So for the key above to be false, the woman must not return the £50. But under the agreement she must. So this yields a contradiction, whether or not Sylvester pays her £1 million; the key cannot be false. On the other hand, if the key is true, then the agreement requires that she keep the £50 … which means that he must pay her £1 million.

“Once we have contradictions involved in conditions,” writes Cave, “we may find ourselves trapped into all manner of things.”

In 1924, as today, it was troublesome and embarrassing to have to excuse your way down a row of theater patrons to get to your seat. Massachusetts inventor Louis Duprey offered this improvement: The whole auditorium is built atop a “loading compartment” where each patron can take his seat, which is then raised on a giant plunger into the theater.

During a performance, any seat occupant may depart by merely turning the handpiece, causing the seat to be lowered into the lobby or loading compartment, and in like manner he may again re-enter the auditorium without in any wise disturbing, or interfering with the view of, other patrons.

A side benefit is that “in case of fire or other panic” all the seats can be lowered into the loading chamber, which is fireproof and designed to accommodate an orderly mass exit. You can even retrieve your hat from the underside of the trapdoor as you take your leave.

UPDATE: Strictly speaking we can’t assume that one of the factors must be 37 — it could be 74, a two-digit multiple of 37. But then when we consider the other factor, the only candidate that yields a product with the pattern TTT is 12, which doesn’t fit. Still, it’s necessary to check this line to be sure the solution is unique. (Thanks, Jeff and Steven.)

Being an angel is hard work. In his 1926 essay “On Being the Right Size,” J.B.S. Haldane writes, “An angel whose muscles developed no more power weight for weight than those of an eagle or a pigeon would require a breast projecting for about four feet to house the muscles engaged in working its wings, while to economize in weight, its legs would have to be reduced to mere stilts.”

And this takes no account of the weight of the harp. In The Book of the Harp, John Marson notes that gold is about 10 times heavier than willow, once the favorite wood of Celtic harp makers. He calculates that a harp of gold would weigh 120 pounds, far more than the 70-80 pounds of the largest pedal harp.

Should we worry about this? Let us not forget that it was angels who destroyed Babylon for its people’s wrongdoings. In the Book of Revelation, chapter 18, verse 21 tells us: “And a mighty angel took up a stone like a great millstone, and cast it into the sea, saying, ‘Thus with violence shall that great city of Babylon be thrown down.'”

This becomes a public health matter. Even if harps aren’t thrown at us deliberately by vengeful angels, Marson writes, “there is always the danger of one being dropped accidentally from a great height, resulting in the kind of damage caused on occasion by meteorites — unless, of course, the Bible is indeed correct after all, and angels do not play harps.”

A pleasing fact from David Wells’ Archimedes Mathematics Education Newsletter:

Draw two parallel lines. Fix a point on one line and move a second point along the other line. If an equilateral triangle is constructed with these two points as two of its vertices, then as the second point moves, the third vertex of the triangle will trace out a straight line.

In the 1920s Bata Kindai Amgoza ibn LoBagola toured the United States and Europe to share the culture of his African homeland with fascinated audiences. The reality was actually much more mundane: His name was Joseph Lee and he was from Baltimore. In this week’s episode of the Futility Closet podcast we’ll tell the curious story of this self-described “savage” and trace the unraveling of his imaginative career.

We’ll also dump a bucket of sarcasm on Duluth, Minnesota, and puzzle over why an acclaimed actor loses a role.

Please consider becoming a patron of Futility Closet — on our Patreon page you can pledge any amount per episode, and all contributions are greatly appreciated. You can change or cancel your pledge at any time, and we’ve set up some rewards to help thank you for your support.

You can also make a one-time donation via the Donate button in the sidebar of the Futility Closet website.

David Killingray and Willie Henderson, “Bata Kindai Amgoza ibn LoBagola and the Making of An African Savage’s Own Story,” in Bernth Lindfors, Africans on Stage: Studies in Ethnological Show Business, 1999.

Site Admin

Info

ABOUT

Futility Closet is a collection of entertaining curiosities in history, literature, language, art, philosophy, and mathematics, designed to help you waste time as enjoyably as possible.

You can read Futility Closet on the web, subscribe by RSS, or sign up to receive a free daily email -- see "Subscribe by Email" in the sidebar.

You can support us by telling your friends about us, leaving a review of the books or podcast on Amazon or iTunes, pledging to our Patreon campaign to support the podcast, or contributing directly via the Donate button in the sidebar above. Thanks!